Problem: As Will is stuck in the Upside Down, he can still communicate with his mom, Joyce, through the Christmas lights (he can turn them on and off with his mind). He can't directly tell his mom where he is, because the monster that took him to the Upside Down will know and relocate him. 

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Thus, he came up with a puzzle to tell his mom his coordinates. His coordinates are the answer to the following problem.

A string consisting only of parentheses ('(' and ')') is called a bracket sequence. Some bracket sequence are called correct bracket sequences. More formally:

  * Empty string is a correct bracket sequence. 
  * if s is a correct bracket sequence, then (s) is also a correct bracket sequence. 
  * if s and t are correct bracket sequences, then st (concatenation of s and t) is also a correct bracket sequence. 



A string consisting of parentheses and question marks ('?') is called pretty if and only if there's a way to replace each question mark with either '(' or ')' such that the resulting string is a non-empty correct bracket sequence.

Will gave his mom a string s consisting of parentheses and question marks (using Morse code through the lights) and his coordinates are the number of pairs of integers (l, r) such that 1 ≤ l ≤ r ≤ |s| and the string slsl + 1... sr is pretty, where si is i-th character of s.

Joyce doesn't know anything about bracket sequences, so she asked for your help.

Input

The first and only line of input contains string s, consisting only of characters '(', ')' and '?' (2 ≤ |s| ≤ 5000).

Output

Print the answer to Will's puzzle in the first and only line of output.

Examples

Input

((?))


Output

4


Input

??()??


Output

7

Note

For the first sample testcase, the pretty substrings of s are:

  1. "(?" which can be transformed to "()". 
  2. "?)" which can be transformed to "()". 
  3. "((?)" which can be transformed to "(())". 
  4. "(?))" which can be transformed to "(())". 



For the second sample testcase, the pretty substrings of s are:

  1. "??" which can be transformed to "()". 
  2. "()". 
  3. "??()" which can be transformed to "()()". 
  4. "?()?" which can be transformed to "(())". 
  5. "??" which can be transformed to "()". 
  6. "()??" which can be transformed to "()()". 
  7. "??()??" which can be transformed to "()()()". 

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;

public class tr0 {
	static PrintWriter out;
	static StringBuilder sb;
	static final double EPS = 1e-9;
	static long mod = 1000000007;
	static int inf = (int) 1e9 + 2;
	static long[] fac;
	static Long[] a;
	static int[] si;
	static ArrayList<Integer> primes;
	static ArrayList<Integer>[] ad;
	static ArrayList<qu>[] d;
	static edge[] ed;
	static int[] l, ch;
	static int[] occ, p;
	static Queue<Integer>[] can;
	static String s;
	static int[] memo;
	static int n, m, k;
	static int[] v;
	static int[] wi;
	static int[] da;
	static long x;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		String s = sc.nextLine();
		int n = s.length();
		int ans = 0;
		int[][] bit = new int[n][n];
		for (int i = 0; i < n; i++) {
			int op = 0;
			int cl = 0;
			int q = 0;
			int p = 0;
			if (s.charAt(i) == ')')
				continue;
			if (s.charAt(i) == '(')
				op++;
			else
				q++;
			p++;
			for (int j = i + 1; j < n; j++) {
				if (s.charAt(j) == '(') {
					op++;
					p++;
					continue;
				}
				if (s.charAt(j) == ')') {
					cl++;
					p--;
				} else {
					p++;
					q++;
				}
				if (p < 0)
					break;
				if ((j - i) % 2 == 0)
					continue;
				// System.out.println(i+" "+j);
				bit[i][j]++;

			}
		}
	//	for(int []a:bit)
		//System.out.println(Arrays.toString(a));
		for (int i = n - 1; i > 0; i--) {
			int op=0;
			int other=1;
			if(s.charAt(i)=='(')
				continue;
               for(int j=i-1;j>=0;j--) {
            	  if(s.charAt(j)=='(')
            		  op++;
            	  else 
            		  other++;
            	  if(other-op<0)
            		  break;
            	  if ((i - j) % 2 == 0)
  					continue;
            	//  System.out.println(i+" "+j+" "+other+" "+op);
            	  if(bit[j][i]==1)
            		  ans++;
               }
		}
		out.print(ans);
		out.flush();
	}

	static class qu implements Comparable<qu> {
		int a;
		int b;

		qu(int y, int g) {
			a = y;
			b = g;
		}

		public String toString() {
			return a + " " + b;
		}

		public int compareTo(qu o) {
			if (a == o.a)
				return b - o.b;
			return a - o.a;
		}
	}

	static class seg implements Comparable<seg> {
		int a;
		int b;
		int l;
		int r;
		int bit;

		seg(int s, int e, int x, int y, int bi) {
			a = s;
			b = e;
			l = x;
			r = y;
			bit = bi;
		}

		public String toString() {
			return a + " " + b + " " + l + " " + r + " " + bit;
		}

		public int compareTo(seg o) {
			// if(a==o.a)
			return bit - o.bit;
			// return
		}
	}

	static class pair implements Comparable<pair> {
		long to;
		long number;

		pair(long t, long n) {
			number = n;
			to = t;
		}

		public String toString() {
			return to + " " + number;
		}

		@Override
		public int compareTo(pair o) {
			if (o.to < to)
				return 1;
			return -1;
		}

	}

	static long modPow(long a, int e)

	{
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1)
				res = (res * a) % mod;
			a = (a * a) % mod;
			e >>= 1;
		}
		return res;
	}

	static long inver(long x) {
		long a = x;
		long e = (mod - 2);
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1) {
				res = ((1l * res * a) % mod);
			}
			a = ((1l * a * a) % mod);
			e >>= 1;
		}
		return res % mod;
	}

	static class edge implements Comparable<edge> {
		int from;
		int to;
		int number;

		edge(int f, int t, int n) {
			from = f;
			to = t;
			number = n;
		}

		public String toString() {
			return from + " " + to + " " + number;
		}

		public int compareTo(edge f) {
			return f.number - number;
		}
	}

	static void seive(int N) {
		si = new int[N];
		primes = new ArrayList<>();
		si[1] = 1;
		for (int i = 2; i < N; i++) {
			if (si[i] == 0) {
				si[i] = i;
				primes.add(i);
			}
			for (int j = 0; j < primes.size() && primes.get(j) <= si[i] && (i * primes.get(j)) < N; j++)
				si[primes.get(j) * i] = primes.get(j);

		}
	}

	static long fac(int n) {
		if (n == 0)
			return fac[n] = 1;
		if (n == 1)
			return fac[n] = 1;
		long ans = 1;
		for (int i = 1; i <= n; i++)
			fac[i] = ans = (i % mod * ans % mod) % mod;
		return ans % mod;
	}

	static long gcd(long a, long b) {

		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static class unionfind {
		int[] p;
		int[] size;
		int[] max;
		int num;

		unionfind(int n) {
			p = new int[n];
			size = new int[n];
			max = new int[n];
			for (int i = 0; i < n; i++) {
				p[i] = i;
				max[i] = i;
			}
			Arrays.fill(size, 1);
			num = n;
		}

		int findSet(int v) {
			if (v == p[v])
				return v;

			max[v] = Math.max(max[v], max[p[v]]);

			p[v] = findSet(p[v]);

			max[v] = Math.max(max[v], max[p[v]]);

			return p[v];
		}

		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}

		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}

		boolean combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			// System.out.println(num+" ppp");
			num--;
			if (size[a] > size[b]) {
				p[b] = a;
				max[a] = Math.max(max[a], max[b]);
				size[a] += size[b];

			} else {
				p[a] = b;
				max[b] = Math.max(max[a], max[b]);
				size[b] += size[a];
			}
			return false;
		}
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}

		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}

		public char nextChar() throws IOException {
			return next().charAt(0);
		}

		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
}